Forces and Laws of Motion Test

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Forces and Laws of Motion Test - 39

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Weekly Quiz Competition

Question 1
1 / -0

A bullet is fired from a gun with a velocity 600 m/s. The recoil velocity of the gun is 3 m/s. What is the ratio of the mass of the gun and bullet ?

A
100:1

B
400:1

C
200:1

D
300:2

Solution

Given,
Initially both Gun and bullet will be in rest ie, initial velocity of Gun and bullet $$=0$$
After fired,
$$V_b=600\ m/s\\V_r=3\ m/s$$
Let mass of gun is $$M$$ and mass of bullet is $$m$$.
Using momentum conservation:
Initial momentum (Before fired)$$=$$ Final momentum (After fired)
$$M\times 0+m\times 0= (-3 \times M) + 600 \times m$$

$$0=-3M+600m$$

$$\Rightarrow \dfrac{M}{m} = \dfrac{600}{3}=\dfrac{200}1$$
Ration of mass of Gun to bullet is $$\dfrac{200}1$$ Option C.
Question 2
1 / -0

A bullet of mass 125 gm leaves a rifle with a velocity of $$500ms^{-1}$$. The rifle recoils with a velocity of $$5ms^{-1}$$. Find the mass of the rifle.

A
100 kg

B
12.5 kg

C
1.25 kg

D
125 kg

Solution

Using linear momentum conservation,
$$m_1u_1+m_2u_2=m_1v_1+m_2v_2$$
$$u_1=u_2=0$$ and $$v_1=-5$$ $$v_2=500$$
Let mass of rifle be $$m$$
$$0 = m \times -5 + 125 \times 500$$
$$m = 12500 gm$$
Mass of rifle $$m=12.5 kg$$
Question 3
1 / -0

The mass of a loaded truck $$10$$ tonnes is going at a speed of $$20 \ kmph$$. A box of mass $$2$$ tonnes slips from it and falls on the road. Find the final velocity of the truck (assume that the power of the engine is constant)?

A
$$2.5\ kmph$$

B
$$25 \ kmph$$

C
$$5.5 \ kmph$$

D
$$3.5\ kmph$$

Solution

When the external force is zero then momentum remains constant.
Using momentum conservation,
Initial momentum$$(P_i)$$ = Final momentum $$(P_f)$$
Momentum = mass $$\times$$ velocity
$$P_i = 10 \times 20$$ ; here units are taken same as given in the question
$$P_f = 8 \times v$$
Now equate momentum-
$$10 \times 20 = 8 \times v$$
$$\Rightarrow v = 25\ kmph $$
Question 4
1 / -0

A bullet of mass $$0.01$$ kg is fired from a gun of mass $$5$$ kg with velocity of $$250$$ m/s, calculate the speed with which the gun recoils.

A
0.50 m/s

B
0.25 m/s

C
0.05 m/s

D
0.025 m/s

Solution

As the net external force on the gun bullet system is zero, the sum of the momentum of the gun and bullet system will be constant.
Now as the gun+bullet system was initially at rest, the initial momentum of the system =-0.
Hence, according to the law of conservation of momentum,
(the final momentum of the bullet fired) + (final momentum of the gun that recoils (opposite direction)) $$=0$$
Momentum of the bullet =$$\left(0.01 \right) \times 250 = 2.5 \ kgm/s$$
Let $$v$$ be the velocity of the recoil of the gun.
Momentum of the recoiling gun =$$\left(5 \right) \times v= 5v \ kgm/s$$
Equating we have $$2.5+5 v=0$$
$$\Rightarrow v=-0.5 \ m/s$$
The speed with which the gun recoils is $$0.50\ m/s$$ in the opposite direction of speed of bullet.
Question 5
1 / -0

Two bodies have masses in the ratio $$3 : 4$$. When a force is applied on the first body, it moves with an acceleration of $$6 \ m/s^2$$. How much acceleration will the same force produce in the second body?

A
$$2.25 \ m/s^2$$

B
$$4.5 \ m/s^2$$

C
$$6 \ m/s^2$$

D
$$5 \ m/s^2$$

Solution

$$Force = mass \times acceleration.$$
So, for a constant force, $$m_1a_1 = m_2a_2$$
$$\displaystyle \implies a_2 = \frac{m_1}{m_2} \times a_1 = \frac{3}{4} \times 6 = 4.5 m/s^2$$
Question 6
1 / -0

Two identical bullets are fired one by a light rifle and another by a heavy rifle with the same force. Which rifle will hurt the shoulder more and why ?

A
Light rifle

B
Heavy rifle

C
Both of them will hurt equally

D
None of these

Solution

The two identical bullets recoil with the same force, but the lighter one will accelerate faster than the heavier one.
We can use Newton's third law to explain better: If $$F_l\ and\ F_H$$ are the forces exerted on the rifles, we have
$$F_l = F_h$$
or $$M_1<M_h$$ and $$a_1 > a_h$$.
The lighter rifle hurts more than a heavier rifle as the acceleration is higher.
Question 7
1 / -0

A passenger in a moving train tosses a coin which falls behind him. It means that the motion of the train is

A
Accelerated

B
Uniform

C
Retarded

D
Along circular tracks
Question 8
1 / -0

The inertia of an object tends to cause the object:

A
$$\text to\ increase\ its\ speed$$

B
$$\text to\ decrease\ its\ speed$$

C
$$\text to\ resist\ any\ change\ in\ its\ state\ of\ motion$$

D
$$\text to\ decelerate\ due\ to\ friction$$

Solution
Question 9
1 / -0

STATEMENT - 1 : Gas ejected from rocket will never exert thrust on the rocket if the ejected gas and the rocket move in the same direction.
STATEMENT - 2 : To exert thrust on rocket in its direction of motion, the ejected gas (w.r.t. rocket) must move opposite to the velocity of rocket (w.r.t. ground).

A
Statement-1 is True, Statement-2 is True ;Statement-2 is a correct explanation for Statement-1.

B
Statement-1 is True, Statement-2 is True ;Statement-2 is NOT a correct explanation for Statement-1.

C
Statement-1 is True, Statement-2 is False.

D
Statement-1 is False, Statement-2 is True.

Solution

Answer is D
If the Gas ejected from rocket and the rocket move in the same direction, even than thrust will be exerted. Hence statement 1 is false.
From Newton' third law, Ejected gas will exert thrust opposite to it. Hence statement 2 is true.
Question 10
1 / -0

An apple falls from a tree because of gravitational attraction between the earth and apple. If $$F_{1}$$ is the magnitude of force exerted by the earth on the apple and $$F_{2}$$ is the magnitude of force exerted by apple on earth, then

A
$$F_{1}$$ is very much greater than $$F_{2}$$

B
$$F_{2}$$ is very much greater than $$F_{1}$$

C
$$F_{1}$$ is only a little greater than $$F_{2}$$

D
$$F_{1}$$ and $$F_{2}$$ are equal

Solution

According to Newton's III law "Every action has an equal and an opposite reaction". An apple falling down has the force of gravity acting downward ($$F_{1}$$) which is the action. The opposite reaction is the force the apple exerts on the earth ($$F_{2}$$).

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Re-Attempt Weekly Quiz Competition

Forces and Laws of Motion Test - 39

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Forces and Laws of Motion Test - 39

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SHARING IS CARING

Question 1

100:1

400:1

200:1

300:2

Solution

Question 2

100 kg

12.5 kg

1.25 kg

125 kg

Solution

Question 3

$$2.5\ kmph$$

$$25 \ kmph$$

$$5.5 \ kmph$$

$$3.5\ kmph$$

Solution

Question 4

0.50 m/s

0.25 m/s

0.05 m/s

0.025 m/s

Solution

Question 5

$$2.25 \ m/s^2$$

$$4.5 \ m/s^2$$

$$6 \ m/s^2$$

$$5 \ m/s^2$$

Solution

Question 6

Light rifle

Heavy rifle

Both of them will hurt equally

None of these

Solution

Question 7

Accelerated

Uniform

Retarded

Along circular tracks

Question 8

$$\text to\ increase\ its\ speed$$

$$\text to\ decrease\ its\ speed$$

$$\text to\ resist\ any\ change\ in\ its\ state\ of\ motion$$

$$\text to\ decelerate\ due\ to\ friction$$

Solution

Question 9

Statement-1 is True, Statement-2 is True ;Statement-2 is a correct explanation for Statement-1.

Statement-1 is True, Statement-2 is True ;Statement-2 is NOT a correct explanation for Statement-1.

Statement-1 is True, Statement-2 is False.

Statement-1 is False, Statement-2 is True.

Solution

Question 10

$$F_{1}$$ is very much greater than $$F_{2}$$

$$F_{2}$$ is very much greater than $$F_{1}$$

$$F_{1}$$ is only a little greater than $$F_{2}$$

$$F_{1}$$ and $$F_{2}$$ are equal

Solution

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